Balanced bipartite distance of $K_4$-free graphs
Combinatorics
2026-05-08 v1
Abstract
We show that every -free graph on vertices can be made balanced bipartite by removing at most edges. This proves a conjecture of Balogh, Clemen, and Lidick\'{y}, and generalizes both Sudakov's result on the bipartite distance of -free graphs and Reiher's result on the sparse half of -free graphs.
Cite
@article{arxiv.2605.05346,
title = {Balanced bipartite distance of $K_4$-free graphs},
author = {József Balogh and Ignacy Buczek and Andrzej Grzesik and Piotr Kuc},
journal= {arXiv preprint arXiv:2605.05346},
year = {2026}
}